time dependent PDE

I have a time dependent problem. The general form is C*du/dt=d2u/dx2 Now C is also changing with t. C=1/D*exp(-A/(b*t+d)+A/d). A, b and d are fixed numbers.

I have the code as below,it works for fixed C=1/D where t=0.but it seems that the C changing with t does not get into co-operated, coz I get the same results with C=1/D*exp(-A/(b*t+d)+A/d) and C=1/D(where t =0) C does not really depend on t from the results.

My question is how to make C depends on t and get the right results.

Thank you! .............................................................

function Desorption2 %dimension unit in mm, s

m = 0;

x = linspace(0,0.1778,100);

t = linspace(0,3550,100);

sol = pdepe(m,@(~,~,~,DuDx) pdex1pde(DuDx,t),@pdex1ic,@pdex1bc,x,t);

% Extract the first solution component as u.

u = sol(:,:,1);

surf(x,t,u)

title('Numerical solution computed with 20 mesh points.')

xlabel('Distance x')

ylabel('Time t')

figure

plot(x,u(end,:))

title(['Solution at t = ' num2str(t(end)) ])

xlabel('Distance x')

ylabel(['u(x,' num2str(t(end)) ')'])

%write results in file

fid = fopen('25C_3550.txt', 'w');

fprintf(fid, '%e\n',x,u(end,:));

fclose(fid);

end

function [c,f,s] = pdex1pde(DuDx,t)

c =1./(1.110e-014*exp(-5327./(0.0417*t+298)+5327/298)*1000000);

f = DuDx;

s = 0;

end

function u0 = pdex1ic(~)

u0 = 0.0001;

end

% -------------------------------------------------------------- function [pl,ql,pr,qr] = pdex1bc(~,ul,~,ur,~)

pl = ul;

ql = 0;

pr = ur;

qr = 0;

end